Extracting ordered patterns from a triangular mesh surface

The last decade has witnessed the proliferation of three-dimensional (3-D) digitizers and scanners as well as substantial developments in techniques for modeling and digitizing 3-D shapes. Basically, shape digitalization can be defined as the process of encoding the surface shape into a discrete format suitable for computing purposes, such as analysis and modeling. Surface tessellation is the backbone of surface digitalization, whereby the surface is encoded by a group of stitched polygons that cover the whole surface. Tessellation can be performed using polygons of any order, but triangles are the most commonly used. Indeed, a triangular mesh is characterized by its simplicity and flexibility. Contrary to other polygons, the triangle is the only polygon in which the vertices are guaranteed to be coplanar. This made triangular mesh the format most supported by graphics software and hardware. Triangular meshes are used in animation, simulation training, architecture, medical and natural sciences, and many other applications.